Extended incomplete gamma functions with applications

An extension of the generalized inverse Gaussian density function is proposed. Analogous to a recent useful generalization of the incomplete gamma functions, extensions of the generalized incomplete gamma functions are presented for which the usual properties and representations are naturally and simply extended. Several classical functions including, Abramowitz's functions, Dowson's integral function, Goodwin and Stalon's function, and astrophysical thermonuclear functions are proved to be special cases of these extensions. In addition, extended Meijer G-functions and Fox's H-functions are defined.